Question

The specific heat of water is approximately............

• A. 4.2 J/kg/K
• B. 4.2 J/g/K
• C. 1 J/kg/K
• D. 1 J/g/K

Hint:

Pay close attention to units in physical constant questions:
- \(4.2 \text{ \textbf{J/g}/K}\) (or \(4.2 \text{ \textbf{J/g}/}^\circ\text{C}\))
- \(4200 \text{ \textbf{J/kg}/K}\) (or \(4.2 \text{ \textbf{kJ/kg}/K}\))
- \(1 \text{ \textbf{cal/g}/}^\circ\text{C}\)

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Specific heat capacity (\(c\)) is defined as the amount of heat energy required to raise the temperature of a unit mass of a substance by one Kelvin (or one degree Celsius).
Water has an exceptionally high specific heat capacity due to its extensive intermolecular hydrogen-bonding network.

Step 2: Detailed Explanation:
The specific heat of liquid water is classically defined as \(1 \text{ calorie per gram per degree Celsius}\) (\(1 \text{ cal/g/}^\circ\text{C}\)).
To convert this into the International System of Units (SI):
\[ 1 \text{ calorie} \approx 4.184 \text{ Joules} \] Therefore, the specific heat capacity of water in grams is:
\[ c \approx 4.184 \text{ J/g/K} \approx 4.2 \text{ J/g/K} \] If expressed per kilogram (the standard SI unit for mass), the value is scaled up by a factor of 1000:
\[ c \approx 4184 \text{ J/kg/K} \approx 4.2 \text{ kJ/kg/K} \] Let us examine the options:
- Option (A) \(4.2 \text{ J/kg/K}\) is incorrect because the unit of mass is kilograms, which makes this value too small by a factor of 1000.
- Option (B) \(4.2 \text{ J/g/K}\) is the correct approximate value.
- Options (C) and (D) represent a specific heat of \(1\), which is only correct if the energy unit is calories (\(1 \text{ cal/g/K}\)), not Joules.

Step 3: Final Answer:
The specific heat of water is approximately \(4.2 \text{ J/g/K}\).